Qr Decomposition Calculator
Result
QR Decomposition — Real 2×2 Matrix — specific, verifiable calculation with defined inputs.
Formula
- Computes a QR factorization for a real 2×2 matrix with a nonzero first column. Q is orthogonal and R is upper triangular; r22 may be negative under this explicit orientation convention. This scoped calculator does not handle matrices of other sizes or matrices whose first column is zero. For a zero first column the calculation appropriately rejects division by zero.
- The main inputs are Matrix a11, Matrix a12, Matrix a21, Matrix a22. Enter them in the units and format shown in the calculator.
- Keep comparable quantities in compatible units whenever the formula combines or compares them.
- Changing any input above recalculates the result with the same calculation engine used by this page.
Example: Qr Decomposition
- Matrix a11: 3
- Matrix a12: 1
- Matrix a21: 4
- Matrix a22: 2
For A=[[3,1],[4,2]], Q=[[0.6,-0.8],[0.8,0.6]], R=[[5,2.2],[0,0.4]].
Sample result: Calculating…
Frequently asked questions
What does the Qr Decomposition calculate?
QR Decomposition — Real 2×2 Matrix — specific, verifiable calculation with defined inputs.
Which values should I enter?
Enter Matrix a11, Matrix a12, Matrix a21, Matrix a22 using the units and format shown beside each field.
What formula does this calculator use?
The calculator uses the following relationship: A = QR, QᵀQ = I. r11 = √(a11²+a21²); q1 = (a11,a21)/r11; q2 = (-a21,a11)/r11; r12 = q1·(a12,a22); r22 = q2·(a12,a22)..
Why might my result differ from another source?
Results can differ when another source uses different units, rounding rules, conventions or assumptions. Compare the inputs and definitions before comparing results.
Does the result update automatically?
Yes. Changing an input updates the result using the same calculation engine shown on this page.